where the second inequality is by Jensen's inequality; the third inequality is since \(K_tS(S^TK_t^2S)^\dagger S^TK_t\)  is a projection matrix.
This shows (a).
(b) follows from (REF ) and the independence among \(\lbrace \zeta _{t,j}\rbrace _j\) .
(c) is proved by [1]}.
